Qiu, Xiu-LiangBodur, MuratCai, Qing-Bo2026-03-102026-03-1020261029-242Xhttps://doi.org/10.1186/s13660-026-03436-5https://hdl.handle.net/20.500.13091/13056This paper mainly introduces (lambda,mu)-Bernstein-Kantorovich-Stancu-B & eacute;zier operators that are a natural continuation of Stancu-type (lambda,mu)-Bernstein-Kantorovich operators constructed by Q.-B. Cai et al. (Enhanced approximation techniques: Stancu-type (lambda,mu)-Bernstein-Kantorovich operators, 2026, https://doi.org/10.21203/rs.3.rs-4689585/v1). For these operators, we first examine the order of approximation in regards to global approximation results using a classical approach, Lipschitz class and the second modulus of continuity. Then, a Voronovskaya-type theorem is provided, which characterizes the asymptotic behavior of these operators. Furthermore, by considering the functions whose first derivatives are of bounded variation, we give the rate of convergence of such operators. Finally, to compare the convergence of such operators both to the (lambda,mu)-Bernstein-Kantorovich-Stancu operators and to themselves for different parameters, we provide some graphical and numerical examples.eninfo:eu-repo/semantics/openAccessBézier OperatorsBounded VariationRate of ConvergenceBézier OperatorsLambda-Bernstein Operators(Lambda, Mu)-Bernstein-Kantorovich-Stancu OperatorsBounded VariationRate of ConvergenceArticle10.1186/s13660-026-03436-52-s2.0-105030183239